(2x%2B3)-(x-1)%5E2-3x(x-5)%3D-44.jpeg "(2x-3)(2x+3)-(x-1)^2-3x(x-5)=-44")
Solving the Equation: (2x-3)(2x+3)-(x-1)^2-3x(x-5)=-44
This article will guide you through the steps to solve the equation (2x-3)(2x+3)-(x-1)^2-3x(x-5)=-44.
Step 1: Expand the expressions.
We begin by expanding the expressions on the left-hand side of the equation:
- (2x-3)(2x+3) is a difference of squares pattern, which expands to 4x² - 9
- (x-1)² expands to x² - 2x + 1
- 3x(x-5) expands to 3x² - 15x
Now our equation looks like this:
4x² - 9 - (x² - 2x + 1) - (3x² - 15x) = -44
Step 2: Simplify the equation.
Next, we simplify the equation by removing the parentheses and combining like terms:
4x² - 9 - x² + 2x - 1 - 3x² + 15x = -44
Combining terms: 0x² + 17x - 10 = -44
Step 3: Isolate the x term.
Now, we want to isolate the x term. Add 10 to both sides of the equation:
17x = -34
Step 4: Solve for x.
Finally, divide both sides by 17 to solve for x:
x = -2
Conclusion
Therefore, the solution to the equation (2x-3)(2x+3)-(x-1)²-3x(x-5)=-44 is x = -2.